Depth of sudden velocity increases from multi-mode Rayleigh waves derived with three-component ambient noise beamforming

Surface wave dispersion curves derived from ambient noise recordings are frequently used to invert for subsurface velocity information. Rayleigh wave ellipticities and phase velocities are exploited, and sometimes jointly inverted, for the velocity structure beneath seismic arrays. Wavelengths of surface waves become large at low frequencies and are, thus, sensitive to great depths, but provide only very smooth velocity profiles. However, sudden velocity increases in the subsurface are of particular interest to delineate the extent of reservoirs, i.e., by sub-horizontal faults or detachments, or estimate the depth of sedimentary basins.

Here, we report a new approach to estimate sudden velocity increases in vertical velocity profiles using Rayleigh wave ellipticities and phase velocities. Using Kepler’s law of motion on elliptical orbits, we can theoretically delineate the frequency-dependent half-height and half-width of the energy ellipse described by Rayleigh waves.

In the presence of sudden velocity increases, fundamental and first higher mode Rayleigh waves have similar phase velocities at the so-called osculation frequency. This often leads to mode misidentification that biases inversion results. We show that this osculation frequency is close to the frequency where the Rayleigh ellipticity of the fundamental mode is one, i.e., motion is circular, and the ellipticity of the first higher mode has its maximum. At this frequency, our derived relation only requires the phase velocity of the first higher mode to estimate the half-height of the ellipse, which is a very good approximation of the depth of the sudden velocity increase.

To derive phase velocities and ellipticities of Rayleigh waves for synthetic three-component waveforms and real-world datasets from three sites (Weisweiler in Germany, FORGE in Utah, USA and Groningen, the Netherlands), we use three-component beamforming, which provides velocity and polarization parameters of recorded waves in short ambient noise time windows and thus can distinguish wave types and modes. From identified Rayleigh waves, we pick the phase velocity of the first higher mode at the osculation frequency directly in the beamformer plots and estimate the depth of sudden velocity increases using our new relation. No inversion scheme is needed for this approach.

This approach provides more accurate depth estimates of velocity jumps than other ambient noise methods. The depth sensitivity is only limited by the inter-station distances in the array configuration and the useable frequency range. The derived depths of sudden velocity increases can be used to constrain inversion schemes for more accurate velocity models or can be used directly to map structural changes in the subsurface.